What are some examples/quotes that illustrate how Hamlet sacrificed his relationship with both Ophelia and his mother?
In Act III, Scene 1, Hamlet is approached by Ophelia who has come to return his love letters. Ophelia is acting against her heart but in obedience to her father and as a pawn of her father and Claudius (who wish to probe the nature of Hamlet's madness). Ophelia has recently been cool to Hamlet, as ordered by Polonius, and Hamlet has been preoccupied with his father's death and his mother's quickie remarriage. Had Ophelia been a Juliet, things would have gone much differently, but as it is, she comes upon Hamlet at a particularly bad moment and becomes his whipping post. After her recent coolness, she is now all sweetness--which to the knowing audience is poignant but to the rejected lover seems coy. In light of how he's feeling about his mother, it seems to him that he has been played by Ophelia, and when he perceives that they are being spied upon, he believes that Ophelia has betrayed him in more than love. Et tu, Brut?
Before King Hamlet's death, there had been speculation that Prince Hamlet might marry "down" by taking Ophelia, a move her father and brother believe is unwise and unlikely but that the queen (at Ophelia's funeral) says she looked forward to. Therefore, when Hamlet strikes back, he hammers at Ophelia's false virtue, her feminine wiles, her drive to breed, and curses any future marriage she might make. Running off at the mouth, he bans all future marriages and then comes back to the one marriage that is at the root of all his madness.
It would seem that Hamlet has burned his bridges with Ophelia. In Scene Two, however, he sits beside her while he observes his mother and Claudius during the play. He might have chosen to sit beside Horatio, but he is like a bitter ex, reluctant to let go. Ophelia doggedly remains civil and reproaches his snarky commentary with restraint. To her retort that the prologue will be brief, he replies, "As a woman's love," summing up his estimation of Gertrude's and Ophelia's fidelity.
From the beginning of the play, Hamlet is disturbed by his mother's apparently insatiable need for sex--why else would she have set aside a decent period of mourning before marrying Claudius? He never considers that she might love Claudius or that reasons of state made the marriage desirable. He seems to think that his masculinely exemplary father must have inspired her love, however briefly, but that Claudius was merely an inexplicable object of her lust. Why would she remarry at all when she might have retired to a convent, like many a chaste widow? Thus the power of the double entendre he directs at Ophelia--a nunnery might either be a convent for the chaste (or honest) or a brothel for the promiscuous (or false).
The Ghost has directed Hamlet to avenge his murder, but Hamlet often seems more deeply preoccupied with his mother's sexual treachery than his uncle's regicide. The Ghost, in fact, does not begrudge Gertrude and intervenes when Hamlet confronts his mother in Act III, Scene four--too late, however, because the damage is done. Hamlet unloads on his mother, accusing her of killing his father and marrying his brother. " Leave wringing of your hands...and let me wring your heart," he says and does. He tells her she is a hypocrite and describes her actions in very brutal words. A terrified (she believes him to be completely and homicidally insane) and guilt-stricken Gertrude pleads for him to stop. "These words like daggers enter in mine ears; no more, sweet Hamlet!" But, as with Ophelia, he just can't seem to stop now that he's really letting her know how he feels, and it takes the Ghost to shut him up. After the Ghost's departure, Hamlet refrains from actively accusing his mother, but sullenly switches to a more passive-aggressive form of castigation, admonishing her to stay out of the king's bed and "Repent what's past...Forgive me this, my virtue; For Virtue itself of vice must pardon beg." Gertrude replies "O, Hamlet! thou hast cleft my heart in twain" to which he recommends throwing away the worser part of it. Good advice, as it turns out, which Gertrude does not accept.
Both the women of Shakespeare's play are criticized by Hamlet for too much sexuality because, according to T. S. Eliot's critique,"sexuality entails danger and violates propriety, or form." Indeed, it is this impropriety of Ophelia and especially Gertrude that Hamlet castigates, and their affections that he repels as an infringement upon morality. For instance, in his first soliloquy, Hamlet complains of his mother,
Fraility, thy name is woman....
...a best that wants discourse of reason
Would have mourned longer--married with my uncle....(1.2.146-148)
and, then, in his second soliloquy,
O most pernicious woman!
O villain, villain, smiling,damned villain! (1.5.105-106)
It is this sexuality of his mother that Hamlet perceives too much that lends itself to an interpretation of his having an Oedipal Complex; however, unlike Oedipus himself, Hamlet does not find his mother's sexuality and lust alluring since he criticizes her relationship with Claudius that is dangerous for the state as it cannot be managed properly. When they speak in her closet [private apartments], Hamlet berates her:
...O shame, where is thy blush?
If thou canst mutine in a matron's bones,
To flaming you let virtue be as wax
And melt in her own fire.....
Nay, but to live
In the rank sweat of an enseamed bed,
Stewed in curruption [sic], honeying and making love
Over the nasty sty---(3.4.82-94)
In similar fashion, Hamlet is repulsed by Ophelia's sexuality because it, too, is dangerous and has been a betrayal. When, for example, Ophelia speaks privately to Hamlet after having been instructed by her father, Polonius, to ascertain if Hamlet is mad. In Act III, Hamlet hints that they have been previously intimate as, knowing that she is speaking with him on the orders of her father after she lies by telling him that Polonius is at home, he asks, "Ha, ha! Are you honest?" (3.1.103), implying that he doubts her love despite her previous sexual actions. Further, Hamlet vents his frustration and ire upon Ophelia because it is as though she exploits her sexuality as a treacherous weapon against him in order to obtain information about him for her father, who will, in turn, pass it on to King Claudius. Thus, his diatribe to Ophelia is also an address to Gertrude:
....God hath given you one face, and you make yourselves another. You jug and amble, and you lisp; you nickname God's creatures, and make your wantonness your ignorance. Go to, I'll no more on't, it hath made me mad. I say we will have no moe [sic] marriage....(3.1.139-145)
Both Gertrude and Ophelia, therefore, are perceived by Hamlet as representative of female corruption. And, since King Hamlet's ghost has told Hamlet not to harm Gertrude, Hamlet speaks through Ophelia to Gertrude, criticizing them both for their improprieties manifested by their sexuality. Hamlet sacrifices his relationship with Gertrude and Ophelia as he disavows them both for their wanton use of their femininity.